A Quartic Quality Loss Function and Its Properties

11,2Department of Industrial and Systems Engineering, North Carolina State University Raleigh, NC 27695-7906, USA

2Department of Industrial and Systems Engineering, North Carolina State University Raleigh, NC 27695-7906, USA

Abstract

We propose a quartic function to represent a family of continuous quality loss functions. Depending on the choice of its parameters the shape of this function within the specification limits can be either symmetric or asymmetric, and it can be either similar to the ubiquitous quadratic loss function or somewhat closer to the conventional step function. We examine this family of loss functions in the context of their industrial applications and use them in a mathematical programming model for the parameter design problem.